2-6-13 M7 Angle relationships and writing multi-step equations to solve for missing angles

1. 2-6-13 M7 Angle relationships and writing multi-step equations to solve for missing angles EQ: What are three reasons you might need to find a missing angle measure? BOP DWP: Harry measured two angles in a triangle with a protractor. The first angle measured 68°, and the second measured 80°. What is the measure of the third angle? A. 22° B. 32° C. 100° D. 122°

2. Harry measured two angles in a triangle with a protractor. The first angle measured 68°, and the second measured 80°. What is the measure of the third angle? A. 22° B. 32° C. 100° D. 122° Answer: B Taken from former Released North Carolina End of Grade Tests Grade 5 Question #26

3. Can I be a triangle? Yes no Yes NO Yes no NO yes Yes

4. Vocabulary quiz 1. Clear desk of all materials except for paper and pencil. 2. Match the word to the definition 3. When everyone is finished, we will check.

5. Angle Relationships These words should be in your folder. Important Vocabulary – • Adjacent Angles: • two angles that share a vertex and a side but no points in their interiors. • Vertical Angles: • angles formed by two intersecting lines, and are opposite each other. Vertical angles are congruent. • Congruent Angles: • angles that have the same measure

6. Angle Relationships Important Vocabulary – • Supplementary Angles: • two angles whose measures add to 180° • Complementary Angles: • two angles whose measures add to 90°

7. USE YOUR WHITEBOARD TO ANSWER THE FOLLOWING QUESTIONS

8. What kinds of angles are shown here? What would be the sum of their measures? 95⁰

9. 80⁰

10. 50⁰

11. 35⁰

12. 88 + 25 + (x - 10) = 180 Solve for x = 77

13. 102 102 + x + 2 + x + 20 = 180 Solve for x 30 x = 28 48

14. Angle Relationships supplementary Example 1: • Find the measure of angle 1 if the measure of angle 4 = 135o • Angles 1 and 4 are _______________ angles. • If they are supplementary angles, they must add up to 180 degrees. Angle 1 measures 45 degrees.

15. Angle Relationships supplementary Example 2: • Find the measure of angles 2, 3, and 4 if 1 = 43o • Angles 1 and 2 are _______________ angles. • If they are supplementary angles, they must add up to 180 degrees. Angle 2 measures 137 degrees.

16. Angle Relationships vertical Example 2 continued: • Find the measure of angles 2, 3, and 4 if the measure of angle 1 = 43o • Angles 1 and 3 are _________ angles. • If they are vertical angles, they must be congruent. Angle 3 measures 43 degrees.

17. Angle Relationships supplementary Example 2 continued: • Find the measure of angles 2, 3, and 4 if measure of angle 1 = 43o • Angles 1 and 4 are _______________ angles. • If they are supplementary angles, they must add up to 180 degrees. Angle 4 measures 137 degrees. Is there another way to find the measure of angle 4 without having to set up an equation?

18. Angle Relationships Example 3 – • Find the measure of each angle • Angle HPM – • 108 degrees • Angle JPI – • 38 degrees

19. Angle Relationships Example 3 – • Find the measure of each angle • Angle IPH – • 34 degrees • Angle KPL – • 34 degrees

20. Complete handout:

24. Summary: Name 2 new things you learned today about triangles Homework: Handout